Optimal Operation of Distribution Networks with Synchronous Generators via Transient Stability Constrained Optimal Power Flow Kamile Fuchs, Roman Kuiava and Thelma S. P. Fernandes Department of Electrical Engineering Federal University of Parana (UFPR) Curitiba, Brazil Email: kamilef@yahoo.com.br, kuiava@eletrica.ufpr.br, thelma@eletrica.ufpr.br Abstract— A common approach to deal with transient stability constraints in optimization problems is the combination of a numerical discretization method with interior point methods (IPMs) for solving large-scale nonlinear programming (NLP). The numerical discretization is adopted to convert the differential equations that describe the electromechanical transients in power systems in a set of algebraic equations to be included into a conventional optimal power flow (OPF) problem. The resulting transient stability constrained optimal power flow (TSC-OPF) problem, however, suffers with the curse of dimensionality, high computational time and memory consumption to solve it, even for small systems. To relieve this computational burden, this paper proposes an algorithm that aims at solving a TSC-OPF problem via primal-dual IPM with only a few time steps of numerical discretization in post-fault period, which is enough to ensure the rotor angle first swing stability. Once the TSC-OPF problem is solved, a numerical discretization method is applied to calculate the system trajectory from the first rotor angle peak in post-fault period. An important contribution of the proposed algorithm is to provide a proper accuracy on the computation of constant admittance loads. Numerical results are obtained for a 9-bus distribution network with the purpose of providing a proper sizing of DG units based on synchronous generators and an optimal operation to the network. I. I NTRODUCTION The connection of distributed generation (DG) units in sub-transmission and distribution networks poses a challenge for the system operation and management in medium and low voltages. With the new environment provided by the inclusion of small generators close to loads, many researches have been focused on certain issues that were not being discussed previously when the distribution networks were basically passive and radial circuits. Some potential impacts of DG units on the distribution operation can be observed, for example, as changes on the power quality and the presence of low-frequency electromechanical oscillations, as discussed in [1]–[5]. Furthermore, an inappropriate siting and sizing of DGs units can cause either under-voltage or over-voltage violations in the distribution feeders [6], as well as, an inadequate transient This work was supported by Institutos LACTEC. response performance of these generators with respect to severe perturbations. In this context, the optimal power flow (OPF) has been an important tool for studies involving the proper locations and sizing of DG units and optimal operation of distribution networks. The set of constraints considered in the OPF is generally determined by only physical and static operational limits. However, in recent years, for reasons of protection against occurrences of severe disturbances, OPF problems involving dynamic security, such as transient stabil- ity constraints, have received considerable research attention, as verified in [7]–[10]. The strategy of incorporating transient stability constraints within an OPF problem poses the challenge of joining time- simulation and optimization. The mathematical modeling of a transient stability constrained optimal power flow (TSC- OPF) becomes very complex due to highly non-linear nature of the differential equations that describes the electromechanical transient behavior of synchronous generators. Another limita- tion is the possibility of incurring a computational convergence problem since the region of feasible solutions becomes very restricted. Based on these considerations, this paper proposes an algorithm that aims at solving a TSC-OPF problem with a minimum number of time steps of numerical discretization in post-fault period, which is enough to ensure the rotor angle first swing stability (FSS). In this paper, the Primal- Dual IPM is incorporated to the proposed algorithm to solve the TSC-OPF. One important contribution of the proposed algorithm is to provide a proper accuracy on the computation of constant admittance loads. The computation of these loads admittances is relevant in the process of solving these opti- mization problems, once that steady-state bus voltages (either magnitude or angle) are dependent variables to be determined by the solution of the TSC-OPF problem, which means they are not previously known for the computation of the system loads admittance. Once the TSC-OPF problem is solved, a numerical discretization method is applied to calculate the system trajectory from the first rotor angle peak in post-fault period. 978-1-4673-8040-9/15/$31.00 ©2015 IEEE